Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

The weekly rental cost of a 20-foot recreational vehicle is \(129.50 plus \)0.15 per mile. 

(a) Find a linear function that expresses the cost C as a function of miles driven m. 

(b) What is the rental cost if 860 miles are driven? 

(c) How many miles were driven if the rental cost is $213.80? 

Step-by-Step Solution

Answer

Part (a). The function is $C\left(m\right)=0.15m+129.50$

Part (b). The rental cost is $258.5$ dollars.

Part (c). 562 miles were driven if the rental cost is 230.80 dollars. 

Step 1. Given information.

The weekly rental cost of a 20-foot recreational vehicle is $129.50 plus $0.15 per mile. 

(a) Find a linear function that expresses the cost C as a function of miles driven m. 

(b) What is the rental cost if 860 miles are driven? 

(c) How many miles were driven if the rental cost is $213.80? 

Part (a) Step 1. Find a linear function that expresses the cost C as a function of miles driven m.

A linear function that expresses the cost C as a function of miles driven m, if it's know that the weekly rental cost of a vehicle is 149.5 dollars plus 0.15 dollars per mile.

The function is :

$C\left(m\right)=0.15m+129.50$  

Part (b) Step 1. Find the rental cost if 860 miles are driven.

The function is given by :

$C\left(m\right)=0.15m+129.50$

The rental cost if the 860 miles are driven:

$C\left(860\right)=0.15\left(860\right)+129.50=129+129.50=258.5$

So, the rental cost is $258.5$ dollars if 860 miles are driven.

Part (c) Step 1. Find out how many miles were driven if the rental cost is $213.80.

The given function is 

$C\left(m\right)=0.15m+129.5$

If the rental cost is $213.80 :

$$\begin{gathered} 213.80=0.15m+129.5 \\ 0.15m=213.80-129.50 \\ 0.15m=84.3 \\ m=\frac{84.3}{0.15}=562 \end{gathered}$$

So, 562 miles were driven if the rental cost is 230.80 dollars.